Space Vector Modulation (SVM) is a modulation technique used for controlling induction, controlling brushless motors, and for generating sinusoidal phase voltages starting from a DC voltage source. This technique is widely used because it allows generation of large sinusoidal voltages with a total harmonic distortion (THD) smaller than classical PWM control techniques.
FIG. 1 depicts a control scheme of a common three-phase motor. By driving the switches of each half-bridge with respective PWM signals, the duty-cycle of which varies with time according to a modulating signal, a generally sinusoidal voltage is applied to each winding of the motor. Typically, the control block CONTROL UNIT includes a standard proportional-integral (PI) controller and a logic circuit that generates the driving signals for the desired control action commanded by the controller. The SVM technique is briefly illustrated hereinbelow.
Space Vector Modulation (SVM) may require a sinusoidal modulation of PWM signals for optimizing the switching pattern of the switches of the half-bridges of the inverter. This technique is characterized by a very good modulation ratio, that is the ratio between the rms value of the modulated wave and the mean value thereof. This technique controls the global behavior of the multi-phase system and not the behavior of each single winding.
The SVM technique has many advantages:
high performances in controlling motors at medium/high speed; high efficiency (about 86%); a good torque control; good performance at start-up of the motor; and regulation of the torque at a constant value with a reduced ripple.
For the case of a three-phase motor, referring to FIG. 2, suppose that in a modulation period a triplet of three-phase voltages is to be applied. This triplet may be represented by the vector VS, the module and phase of which are V and γ respectively, that is comprised between two generic configurations VK and VK+1 of the six possible active configurations of the inverter that drives the motor. Application of the vector VS is done by applying the vector VK (that in FIG. 2 is V1) for a time α, the vector VK+1 (that in FIG. 2 is V2) for a time β and a null vector V0 (000 or 111, are not depicted in FIG. 2) for a time δ, such that in a PWM period the mean value of the voltage equals the vector VS.
The intervals during which the vectors Vk, Vk+1 and V0 are applied are those that verify the following integral equation:
                                          ∫            0                          Δ              ⁢                                                          ⁢              T                                ⁢                                                    V                _                            s                        ⁢                                                  ⁢                          ⅆ              t                                      =                                            ∫              0              α                        ⁢                                                            V                  _                                k                            ⁢                                                          ⁢                              ⅆ                t                                              +                                    ∫              0              β                        ⁢                                                            V                  _                                                  k                  +                  1                                            ⁢                                                          ⁢                              ⅆ                t                                              +                                    ∫              0              δ                        ⁢                                                            V                  _                                0                            ⁢                                                          ⁢                              ⅆ                t                                                                        (        1        )            wherein ΔT is the PWM period and α, β and δ are the turn-on times of the upper switches of the inverter. This equation is solved considering that Vk and Vk+1 are constant in a module for each of the six sectors, and VS is constant within a PWM period. Equation (1) becomes: VS·ΔT= Vk·α+ Vk+1·β+ V0·δα+β+δ=ΔT  (2)Considering that V0=0, it is:
                              β          =                                    2                              3                                      ⁢                                          V                ⁢                                                                  ⁢                sin                ⁢                                  (                                      γ                    -                                          γ                      k                                                        )                                                            V                k                                      ⁢            Δ            ⁢                                                  ⁢            T                          ⁢                                  ⁢                  α          =                                                                      V                  ⁢                                                                          ⁢                                      cos                    ⁡                                          (                                              γ                        -                                                  γ                          k                                                                    )                                                                                        V                  k                                            ⁢              Δ              ⁢                                                          ⁢              T                        -                          β              2                                      ⁢                                  ⁢                  δ          =                                    Δ              ⁢                                                          ⁢              T                        -            α            -            β                                              (        3        )            being γ the angle of the phasor VS that represents the triplet of voltages to be applied to the motor and γk is the angle of the phasor Vk.
After having calculated the conduction times, it is necessary to establish the strategy with which the vectors Vk, Vk+1 and V0 are applied. The simplest way is to sequentially establish the conduction times α, β and γ in a period ΔT, as depicted in FIG. 3.
This approach has several drawbacks: uneven switching frequency of the electronic components; and the possibility of simultaneous switching of two half-bridges with a consequent increase of power losses.
The above problems are prevented by properly subdividing each conduction period according to a so-called seven states logic, illustrated in FIG. 4, that allows switching a half-bridge at the time. The same observation made for the first sector holds, with the respective differences having been considered, when the phase γ is in the second sector. Of course, in this case, α is not referred to V1 but to V2. This implies that it may be necessary to take into account the sector to which the phase angle γ currently belongs for calculating the correct switching pattern, and thus for correctly carrying out the SVM algorithm. To determine the sector of pertinence, it is necessary to know the phase of the reference vector, that may be calculated with the following formula:
                    γ        =                  arctan          ⁡                      (                                                          ⁢                m                ⁢                                  (                                                            V                      _                                        s                                    )                                                                            ⁢                                  e                  ⁡                                      (                                          V                      s                                        )                                                                        )                                              (        4        )            wherein the operators m(.) and e(.) produce the imaginary part and the real part of their argument.
If α, β and δ are known, it is possible to calculate the respective duty-cycles t1, t2, t3 of the high-side of each half-bridge of the inverter using a look-up table that implements the seven-states logic for each sector, as shown in the following table 1:
Sector 0Sector 1Sector 2t1      δ    4    ΔT            β      2        +          δ      4        ΔT            ΔT      2        -          δ      4        ΔT t2            α      2        +          δ      4        ΔT      δ    4    ΔT      δ    4    ΔT t3            ΔT      2        -          δ      4        ΔT            ΔT      2        -          δ      4        ΔT            α      2        +          δ      4        ΔTSector 3Sector 4Sector 5t1            ΔT      2        -          δ      4        ΔT            α      2        +          δ      4        ΔT      δ    4    ΔT t2            β      2        +          δ      4        ΔT            ΔT      2        -          δ      4        ΔT            ΔT      2        -          δ      4        ΔT t3      δ    4    ΔT      δ    4    ΔT            β      2        +          δ      4        ΔT
By comparing (FIG. 5), a triangular modulating signal with three thresholds ta, tb and tc, the six PWM driving signals aH, bH and cH and aL, bL and cL, (H=high-side, L=low-side) that drive the inverter are obtained, as shown in FIG. 5, with respective duty-cycles t1, t2, t3.
The above described procedure implements a so-called PWM center aligned modulation, that implies a symmetry around the mid-point of the PWM period. This configuration produces in each period two pulses line-to-line with the modulating signal. Thus, the effective switching frequency is doubled, with the effect of reducing the ripple of current without the drawback of incrementing the dynamical power consumption of the switching devices of the inverter.
In FIG. 5, the letters a, b, c indicate the first, second and third branch of the inverter, the letter H indicates the high-side switches, and the letter L indicates the low-side switches. FIG. 5 is only a basic scheme that does not accounts for the dead time, that is the time in which both switches must be off for preventing shorts between the supply and ground. The technique is illustrated in greater detail in Shinohara, “Comparison Between Space Vector Modulation and Subharmonic Methods for Current Harmonics of DSP-Based Permanent-Magnet AC Servo Motor Drive System”, Sun et al., “Optimized Space Vector Modulation and Regular-Sampled PWM”, Chen et al, “A New Space Vector Modulation Technique for Inverter Control”, and Zhou et al., “Relationship Between Space-Vector Modulation Technique for Inverter Control.”
The SVM technique described above is usually implemented via software by DSPs or microcontrollers equipped with dedicated peripherals. In Rathnakumar et al., “A New Software Implementation of Space Vector PWM”, classic software implementations using Matlab and Psim are described that show the great complexity of the calculations required for a correct implementation of the SVM.
In “Optimized Space Vector Modulation and Overmodulation with the XC866”, Infeon Application Note AP0803620, V 2.0, a software implementation with an 8-bit microcontroller is shown. In order to make the calculation of the SVM easier, the symmetry about angles of 60° intrinsic to the SVM are exploited, and the values of the sine and cosine functions are stored in a look-up table (LUT). A similar approach is presented also in Copeland, “Generate Advanced PWM Signals Using 8-bit mCs”. Also hardware implementations of the SVM are disclosed in the literature. A possible hardware implementation, particularly for implementing a PWM using a Time Processor Unit (TPU) of the microcontroller Motorola 68HC16 is illustrated in Ahmad et al., “Comparison of Space Vector Modulation Techniques Based on Performance Indexes and Hardware Implementation”. In Attaianese et al, “A Low Cost Digital SVM Modulator with Dead Time Compensation”, a hardware system input with the values of duty-cycles calculated by the microcontroller for carrying out the SVM and correctly driving the inverter, and even compensating the dead time, is described.
In Takahashi et al., “Implementation of Complete AC Servo Control in a Low Cost FPGA and Subsequent ASSP Conversion”, a hardware FPGA implementation of a complete control system implementing a so-called Field Oriented Control (FOC) technique is disclosed. The document also discloses a hardware implementation of SVM. This approach has been commercially implemented in two integrated circuits marketed by International Rectifier “High Performance Configurable Digital AC Servo Control IC”, International Rectifier DataSheet No. PD60224 Rev. B, and “High Performance Sensorless Motion Control IC”, International Rectifier DataSheet No. PD60225 Rev. B.